The Phillips Curve Describing an Economy Takes the Form U $\alpha$

The Phillips curve describing an economy takes the form u = uⁿ - $\alpha$ ( $\pi$ - E $\pi$ ) . The central bank directly sets the inflation rate to minimize the following loss function, L(u, $\pi$ ) = u + $\gamma$ $\pi$ ². The symbol u denotes the unemployment rates, uⁿ is the natural rate of unemployment, $\pi$ is the inflation rate, E $\pi$ is the expected inflation rate, and $\alpha$ and $\gamma$ are behavioral response parameters of the economy. Private agents form their expectations rationally before the central bank sets the inflation rate. The optimal inflation rate when the central bank operates using a fixed rule will be ______. The optimal inflation rate when the central bank operates with discretion will be ______.

A) uⁿ; 0
B) 0; uⁿ
C) 0; $\alpha$ /(2 $\gamma$ )
D) $\alpha$ /(2 $\gamma$ ) ; 0